I think "A language often involved in the process of making computer programs" is way too weak to define a "Programming language". A programming language at least needs to have state/expressions/logic. I'm sure there is a good definition, but if we allow html then any markup is programming and that's obviously false so the line has to be drawn somewhere.

The reason this debate is so strange is because some people think it's gatekeeping to say someone who writes html for a living isn't "programming". It's nonsense.